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Trees of manifolds as
boundaries of spaces and groups
Jacek Świątkowski |
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Geometry & Topology 24 (2020) 593–622
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Abstract |
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We show that trees of manifolds, the topological spaces introduced by Jakobsche, appear as boundaries at infinity of various spaces and groups. In particular, they appear as Gromov boundaries of some hyperbolic groups, of arbitrary dimension, obtained by the procedure of strict hyperbolization. We also recognize these spaces as boundaries of arbitrary Coxeter groups with manifold nerves and as Gromov boundaries of the fundamental groups of singular spaces obtained from some finite-volume hyperbolic manifolds by cutting off their cusps and collapsing the resulting boundary tori to points. |
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Keywords
hyperbolic group, Gromov boundary
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Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F65, 57M07
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References |
Publication
Received: 25 April 2013
Revised: 19 January 2016
Accepted: 6 August 2019
Published: 23 September 2020
Proposed: Steve Ferry
Seconded: John Lott, Bruce Kleiner
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Authors |
| Jacek Świątkowski | |
| Instytut Matematyczny Uniwersytet Wrocławski Wrocław Poland |
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